The accretion disk around a white dwarf is made of hydrogen accumulated from a companion. This would eliminate neutron stars and black holes, as they do not have any hydrogen remaining. A protostar and a giant would both be made of hydrogen (in the case of giants, in their outer layers), but a companion close enough to transfer material would need to have been born at the same time as the white dwarf. This makes it very unlikely that the companion star would be a low-mass protostar that has not even started its main-sequence lifetime, yet close enough to transfer hydrogen to the white dwarf. It would be much more likely that the companion star would have been a slightly less massive medium-mass star that has already gone through its main-sequence lifetime, and as a giant expanded its outer layers enough such that the white dwarf (which started as a slightly more massive medium-mass star) can begin accretion.

(This infalling hydrogen collects into an accretion disk surrounding the white dwarf, and due to Kepler's third law, the outer part of the disk orbits slower than the inner part of the disk. Due to the density of the disk, the difference in speeds between adjacent parts causes friction, producing enough heat for the disk to become incandescent, thus emitting blackbody radiation that peaks in the x-ray portion of the electromagnetic spectrum.)